English

Modular groups and planar maps

Number Theory 2020-10-06 v2 Algebraic Geometry Group Theory

Abstract

In this paper we give an explicit formula for the number of subgroups of the modular group of a given index that are genus zero and torsion-free and a formula for their conjugacy classes. We do so by exhibiting a correspondence between these groups and the trivalent maps on a sphere. We focus on the particular case of the subgroups of index 18 which have some interesting geometric properties.

Keywords

Cite

@article{arxiv.1910.03050,
  title  = {Modular groups and planar maps},
  author = {Abdellah Sebbar and Khalil Besrour},
  journal= {arXiv preprint arXiv:1910.03050},
  year   = {2020}
}

Comments

Few typos have been corrected in the references

R2 v1 2026-06-23T11:36:56.367Z